As you know Continental was in Chapter 11 Bankruptcy about a decade ago. How did the new CEO get this huge airline out of this difficult situation and return it into profitability. Your knowledge will assist me!

Three words: GO FORWARD PLAN.
They brought in the right person (Gordon) at the right time. People felt that he was honest compared to some of his predecessors.
He developed a great plan and threw out everything which was unprofitable. But I think the most important thing was that he changed the employee morale. The staff was proud again to work for CO. He gave out on time bonuses to the whole staff and profit sharing. He furthermore made some nice deals with Boeing, his former employer.
If you read his book "From worst to first" you will find a lot more points.

When Gordon came to CO, the environment was much different than today, so it was much easier in order to return to profitability. Back in 1993/1994, it was possible to be profitable if you had the right operation set up.

Today, it seems as if it's impossible for any of the legacy carriers to get their feet on the ground, so doing the same with a bankruptcy today would be extremely difficult.

You get out of bankruptcy by taking your business plan to the bank or creditors, getting a loan to get you started anew and then cut waste, large salaries, people who are not needed, renegotiate ALL contracts and if you are lucky(and good) the court over a period of time, lets you come out of bankruptcy. This is how its done, airline or any business.
safe